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29 Mar 2021, 02:00
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
77% (00:32) correct
23%
(00:50)
wrong
based on 141
sessions
History
Date
Time
Result
Not Attempted Yet
What is the value of the greatest positive integer \(x\), such that \(3^x\) is a divisor of \(10!\)
A. 1
B. 2
C. 3
D. 4
E. 5
A. 1
B. 2
C. 3
D. 4
E. 5
29 Mar 2021, 02:57
Kudos
Bookmarks
What is the value of the greatest positive integer x, such that 3^x is a divisor of 10!
3 is the prime number, we need to check the highest power 3 as a factor in 10!
10/3+10/3^2+10/3^3...
3.33+1.11.+0....
4
Highest power of 3 in 10! can be 4.
D is the correct answer in my opinion
3 is the prime number, we need to check the highest power 3 as a factor in 10!
10/3+10/3^2+10/3^3...
3.33+1.11.+0....
4
Highest power of 3 in 10! can be 4.
D is the correct answer in my opinion
31 Mar 2021, 08:11
Kudos
Bookmarks
Solution
Given
- • We are not given anything in the question statement.
To find
We need to determine
- • the value of the greatest positive integer x, such that 3x is a divisor of 10!
Approach and Working out
- • The greatest integer x such that 3x is a divisor of 10! will be equal to the number of 3s in the prime factorization of 10!
• To find this, we successively divide 10 by 3 and its powers and add up the quotients from these division calculations.
- o 10 divided by 3
- 10 = 3 x 3 + 1
Quotient = 3
- o 10 divided by \(3^2 \)
- 10 = 9 x 1 + 1
Quotient = 1
Thus, option D is the correct answer.
Correct Answer: Option D
